As I understand it, a mourner says kadish to declare that despite his loss he still praises God and understands that this was God's will.
It's sanctification of G-d's name to help fill the void by one less person alive, and for the deceased's merit.
Tziduk hadin -- the blessing said proclaiming G-d "the judge of truth", has some of the psychological aspects you're describing -- and is only said by the mourner (or other person intensely affected).
Certainly if a mourner uses kaddish as their form of expression of accepting G-d's plans, that's wonderful; but it's not "what kaddish is about." (Another explanation of Kaddish is that it may have been a way to enable more people to do something meritorious if they couldn't all lead the services, which was the older recommended practice.)
So if someone is unable to say Kaddish but a friend does in their stead (or they pay for someone to do it), there is still a sanctification of G-d's Name being made, despite the loss of life (and in the deceased's merit).
In cases where the mourner truly can't say Kaddish for whatever reason, the practice of paying someone to do it (though it seems weird from a religious perspective) is regarded as quite old (several centuries) and strong -- there have been points in time where if not for it, yeshiva students wouldn't have been able to eat.